Compensating the Distributed Effect of Diffusion and Counter-Convection in Multi-Input and Multi-Output LTI Systems
Compensation of infinite-dimensional input or sensor dynamics in SISO, LTI systems is achieved using the backstepping method. For MIMO, LTI systems with distributed input or sensor dynamics, governed by diffusion with counter-convection, we develop a methodology for constructing control laws and obs...
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| Veröffentlicht in: | IEEE transactions on automatic control 2011-03, Vol.56 (3), p.637-643 |
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| container_title | IEEE transactions on automatic control |
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| creator | Bekiaris-Liberis, N Krstic, M |
| description | Compensation of infinite-dimensional input or sensor dynamics in SISO, LTI systems is achieved using the backstepping method. For MIMO, LTI systems with distributed input or sensor dynamics, governed by diffusion with counter-convection, we develop a methodology for constructing control laws and observers that compensate the infinite-dimensional actuator or sensor dynamics. The explicit construction of the compensators are based on novel transformations, which can be considered of "backstepping-forwarding" type, of the finite-dimensional state of the plant and of the infinite-dimensional actuator or sensor states. Based on these transformations we construct explicit Lyapunov functionals which prove exponential stability of the closed-loop system, or convergence of the estimation error in the case of observer design. Finally, we illustrate the effectiveness of our controller with a numerical example. |
| doi_str_mv | 10.1109/TAC.2010.2091187 |
| format | Article |
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For MIMO, LTI systems with distributed input or sensor dynamics, governed by diffusion with counter-convection, we develop a methodology for constructing control laws and observers that compensate the infinite-dimensional actuator or sensor dynamics. The explicit construction of the compensators are based on novel transformations, which can be considered of "backstepping-forwarding" type, of the finite-dimensional state of the plant and of the infinite-dimensional actuator or sensor states. Based on these transformations we construct explicit Lyapunov functionals which prove exponential stability of the closed-loop system, or convergence of the estimation error in the case of observer design. 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| ispartof | IEEE transactions on automatic control, 2011-03, Vol.56 (3), p.637-643 |
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| source | IEEE Electronic Library (IEL) |
| subjects | Actuators Aerodynamics Applied sciences Backstepping Boundary conditions Computer science control theory systems Construction Control system analysis Control system synthesis Control theory. Systems Diffusion Dynamical systems Dynamics Eigenvalues and eigenfunctions Equations Exact sciences and technology Laws Modelling and identification Multiple-input multiple-output (MIMO) Observers Sensors Transformations |
| title | Compensating the Distributed Effect of Diffusion and Counter-Convection in Multi-Input and Multi-Output LTI Systems |
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